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Distributive property. In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra . For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition .
G. H. Hardy, A Mathematician's Apology (1940) He [Russell] said once, after some contact with the Chinese language, that he was horrified to find that the language of Principia Mathematica was an Indo-European one. John Edensor Littlewood, Littlewood's Miscellany (1986) The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by ...
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
Among many uses, it gives a simple proof of the AM–GM inequality in two variables. The proof holds in any commutative ring. Conversely, if this identity holds in a ring R for all pairs of elements a and b, then R is commutative. To see this, apply the distributive law to the right-hand side of the equation and get
Pascal's law (also Pascal's principle [1] [2] [3] or the principle of transmission of fluid-pressure) is a principle in fluid mechanics given by Blaise Pascal that states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. [4]
v. t. e. The Rule in Shelley's Case is a rule of law that may apply to certain future interests in real property and trusts created in common law jurisdictions. [ 1]: 181 It was applied as early as 1366 in The Provost of Beverly's Case[ 1]: 182 [ 2] but in its present form is derived from Shelley's Case (1581), [ 3] in which counsel stated the ...
Arrow's theorem establishes that no ranked voting rule can always satisfy independence of irrelevant alternatives, but it says nothing about the frequency of spoilers. This led Arrow to remark that "Most systems are not going to work badly all of the time. All I proved is that all can work badly at times."
Higher category: Law and Common law. v. t. e. Waste is a term used in property law to describe a cause of action that can be brought in court to address a change in condition of real property brought about by a current tenant that damages or destroys the value of that property. A lawsuit for waste can be brought against a life tenant or lessee ...